Funny, no one in my family has psoriasis. I'm one of those cases that just popped up.
Maybe you should find something that controls the itch for you. For me regular mouthwash worked great, especially on my scalp. I'd go and buy a bottle of Listerine and soak my scalp untill the itching went away. Aahhhh... Other things that I've tried are: aloe vera gel with tea tree oil, gold bond lotion (a mess on my head, lol), mint tea, witch hazel, peroxide and alcohol. Some of them work great, some work a little, but I liked mouthwash best.